广西师范大学学报（自然科学版） ›› 2017, Vol. 35 ›› Issue (3): 75-82.doi: 10.16088/j.issn.1001-6600.2017.03.009

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带p-Laplacian算子的时滞分数阶微分方程边值问题3个正解的存在性

闫荣君, 韦煜明*, 冯春华   

  1. 广西师范大学数学与统计学院,广西桂林541004
  • 出版日期:2017-07-25 发布日期:2018-07-25
  • 通讯作者: 韦煜明(1974—),男,广西桂平人,广西师范大学教授,博士。E-mail :ymwei@gxnu.edu.cn
  • 基金资助:
    国家自然科学基金(11361010);广西自然科学基金(2014GXNSFAA118002);广西高等学校高水平创新团队及卓越学者计划;广西高等数学与统计模型重点实验室开放基金

Existence of Three Positive Solutions for Fractional Differential Equation ofBoundary Value Problem with p-Laplacian Operator and Delay

YAN Rongjun, WEI Yuming*, FENG Chunhua   

  1. College of Mathematics and Statistics, Guangxi Normal University,Guilin Guangxi 541004, China
  • Online:2017-07-25 Published:2018-07-25

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摘要： 本文研究一类带p-Laplacian算子的分数阶时滞微分方程边值问题正解的存在性,应用Avery-Peterson不动点定理,当非线性项f满足一定增长条件时,得到上述边值问题至少存在3个正解的充分条件,得到一些新的结果,推广了已有的工作。

关键词: 分数阶微分方程, 时滞微分方程, 边值问题, p-Laplacian算子, Avery-Peterson不动点定理

Abstract: In this paper,the existence of positive solutions for fractional differential equation boundary value problems with p-Laplacian operator and delay are considered. By using Avery-Perterson fixed point theorem,under certain growth conditions, the existence of at least three positive solutions for the above boundary value problem are studied. Not only are some new results obtained,but also some known results are generalized and improved.

Key words: fractional differential equation, delay, boundary value problem, p-Laplacian operator, Avery-Peterson fixed point theorem

中图分类号: 

  • O175.8
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